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Difficult integral


I need to calculate the following integral

Integrate [(Sin[x])^2 rho Exp[I n x],{x,0,2 Pi}]

as a function of the two parameters rho and n. I have tried it
for rho = 1, 4, 8, 10, and it works, but it doesn't work at all
for rho = 12. I left the computer on all night but only got the
same expression as a result.
Any suggestions?
Thanks

Marco


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